Multiply the following complex numbers: $({-5+4i}) \cdot ({-3-2i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-5+4i}) \cdot ({-3-2i}) = $ $ ({-5} \cdot {-3}) + ({-5} \cdot {-2}i) + ({4}i \cdot {-3}) + ({4}i \cdot {-2}i) $ Then simplify the terms: $ (15) + (10i) + (-12i) + (-8 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 15 + (10 - 12)i - 8i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 15 + (10 - 12)i - (-8) $ The result is simplified: $ (15 + 8) + (-2i) = 23-2i $